In the multi-head attention mechanism of the transformer, why do we need both $W_i^Q$ and ${W_i^K}^T$?
I'll use notation from the paper you cited, and any other readers should refer to the paper (widely available) for definitions of notation.  The utility of using $W^Q$ and $W^K$, rather than $W$, lies in the fact that they allow us to add fewer parameters to our architecture.  $W$ has dimension $d_{model} \times d_{model}$, which means that we are adding $d_{model}^2$ parameters to our architecture.  $W^Q$ and $W^K$ each have dimension $d_{model} \times d_k$, and $d_k=\frac{d_{model}}{h}$. If we use these two matrices, we only add $2\frac{d_{model}^2}{h}$ parameters to our architecture, even though their multiplication (with the transpose) allows us to have the correct dimensions for matrix multiplication with $Q$ and $K$.
We do use $h$ attention heads, which then brings our number of parameters back up, but the multiple heads let the model attend to different pieces of information in our data.